Abstract

We use a collective-variable approach to study the dynamical behavior of vector solitons in the Manakov system under strong environmental perturbations induced by the fiber losses and a modified cross-phase modulation parameter. We identify and discuss the salient features associated with energy-exchange collisions of transmissional and reflectional types. Particularly, we find that such perturbations can induce important effects not only on fundamental soliton parameters such as the peak power, central position, width, chirp, and frequency, but also on the nature of the collision. Interestingly, we find that the perturbations lead to only a slight alteration of collision-induced energy-switching processes. A property of high robustness of the energy-exchange collision of the Manakov vector solitons is thus demonstrated.

© 2007 Optical Society of America

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  1. Yu. S. Kivshar and G. P. Agrawal, Optical Solitons, 2nd ed. (Academic, 2003).
  2. G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, 1995).
  3. A. Hasegawa and Y. Kodama, Solitons in Optical Communications (Oxford U. Press, 1995).
  4. S. V. Manakov, "On the theory of two-dimensional stationary self-focusing of electomagnetic waves," Sov. Phys. JETP 38, 248-253 (1974).
  5. R. Radhakrishnan, M. Lakshmanan, and J. Hietarinta, "Inelastic collision and switching of coupled bright solitons in optical fibers," Phys. Rev. E 56, 2213-2216 (1997).
    [CrossRef]
  6. Y. Bard and Y. Silberberg, "Polarization evolution and polarization instability of solitons in birefringent optical fibers," Phys. Rev. Lett. 78, 3290-3293 (1997).
    [CrossRef]
  7. J. U. Kang, G. I. Stegeman, J. S. Aitchison, and N. Akhmediev, "Observation of Manakov spatial solitons in AlGaAs planar waveguides," Phys. Rev. Lett. 76, 3699-3702 (1996).
    [CrossRef] [PubMed]
  8. Z. Chen, M. Segev, T. H. Coskun, D. N. Christodoulides, and Y. S. Kivshar, "Coupled photorefractive spatial-soliton pairs," J. Opt. Soc. Am. B 14, 3066-3077 (1997).
    [CrossRef]
  9. J. Babarro, M. J. Paz-alonso, H. Michinel, J. R. Salgueiro, and D. N. Olivieri, "Controllable scattering of vector Bose-Einstein solitons," Phys. Rev. A 71, 043608 (2005).
    [CrossRef]
  10. C. Anastassiou, J. W. Fleischer, T. Carmon, M. Segev, and K. Steiglitz, "Information transfer through cascaded collisions of vector solitons," Opt. Lett. 26, 1498-1500 (2001).
    [CrossRef]
  11. M. H. Jakubowski, K. Steiglitz, and R. Squier, "State transformations of colliding optical solitons and possible application to computation in bulk media," Phys. Rev. E 58, 6752-6758 (1998).
    [CrossRef]
  12. E. Feigenbaum and M. Orenstein, "Coherent interactions of colored solitons via parametric processes: modified perturbation analysis," J. Opt. Soc. Am. B 22, 1414-1423 (2005).
    [CrossRef]
  13. A. A. Sukhorukov and N. N. Akhmediev, "Multiport soliton devices with controllable transmission," Opt. Lett. 28, 908-910 (2003).
    [CrossRef] [PubMed]
  14. N. Lazarides and G. P. Tsironis, "Coupled nonlinear Schrödinger field equations for electromagnetic wave propagation in nonlinear left-handed materials," Phys. Rev. E 71, 036614 (2005).
    [CrossRef]
  15. T. Kanna and M. Lakshmanan, "Exact soliton solutions, shape changing collisions, and partially coherent solitons in coupled nonlinear Schrödinger equations," Phys. Rev. Lett. 86, 5043-5046 (2001).
    [CrossRef] [PubMed]
  16. T. Kanna and M. Lakshmanan, "Exact soliton solutions of coupled nonlinear Schrödinger equations: shape changing collisions, logic gates, and partially coherent solitons," Phys. Rev. E 67, 046617 (2003).
    [CrossRef]
  17. K. Steiglitz, "Time-gated Manakov spatial solitons are computationally universal," Phys. Rev. E 63, 016608 (2000).
    [CrossRef]
  18. M. J. Ablowitz, B. Prinari, and A. D. Trubatch, "Soliton interaction in the vector NLS equations," Inverse Probl. 20, 1217-1237 (2004).
    [CrossRef]
  19. R. Radhakrishnan, P. Tchofo Dinda, and G. Millot, "Efficient control of the energy-exchange due to the Manakov vector-soliton collision," Phys. Rev. E 69, 046607 (2003).
    [CrossRef]
  20. Y. Kodama and M. J. Ablowitz, "Perturbations of solitons and solitary waves," Stud. Appl. Math. 64, 225-245 (1981).
  21. V. I. Karpman and V. V. Solovev, "A perturbational approach to the two soliton system," Physica D 3, 487-502 (1981).
    [CrossRef]
  22. V. S. Schesnovich and E. V. Doktorov, "Perturbation theory for solitons of the Manakov system," Phys. Rev. E 55, 7626-7635 (1997).
    [CrossRef]
  23. T. I. Lakoba and D. J. Kaup, "Perturbation theory for the Manakov soliton and its applications to pulse propagation in randomly birefringent fibers," Phys. Rev. E 56, 6147-6165 (1997).
    [CrossRef]
  24. J. Yang, "Multisoliton perturbation theory for the Manakov equations and its applications to nonlinear optics," Phys. Rev. E 59, 2393-2405 (1999).
    [CrossRef]
  25. J. Yang, "Interactions of vector solitons," Phys. Rev. E 64, 026607 (2001).
    [CrossRef]
  26. D. Anderson, "Variational approach to nonlinear pulse propagation in optical fibers," Phys. Rev. A 27, 3135-3145 (1983).
    [CrossRef]
  27. P. Tchofo Dinda, K. Nakkeeran, and A. B. Moubissi, "Collective variable theory for optical solitons in fibers," Phys. Rev. E 64, 016608 (2001).
    [CrossRef]
  28. P. Tchofo Dinda, G. Millot, E. Seve, and M. Haelterman, "Demonstration of a nonlinear gap in the modulational instability spectra of wave propagation in highly birefringent fibers," Opt. Lett. 21, 1640-1642 (1996).
    [CrossRef]

2005 (3)

J. Babarro, M. J. Paz-alonso, H. Michinel, J. R. Salgueiro, and D. N. Olivieri, "Controllable scattering of vector Bose-Einstein solitons," Phys. Rev. A 71, 043608 (2005).
[CrossRef]

N. Lazarides and G. P. Tsironis, "Coupled nonlinear Schrödinger field equations for electromagnetic wave propagation in nonlinear left-handed materials," Phys. Rev. E 71, 036614 (2005).
[CrossRef]

E. Feigenbaum and M. Orenstein, "Coherent interactions of colored solitons via parametric processes: modified perturbation analysis," J. Opt. Soc. Am. B 22, 1414-1423 (2005).
[CrossRef]

2004 (1)

M. J. Ablowitz, B. Prinari, and A. D. Trubatch, "Soliton interaction in the vector NLS equations," Inverse Probl. 20, 1217-1237 (2004).
[CrossRef]

2003 (3)

R. Radhakrishnan, P. Tchofo Dinda, and G. Millot, "Efficient control of the energy-exchange due to the Manakov vector-soliton collision," Phys. Rev. E 69, 046607 (2003).
[CrossRef]

T. Kanna and M. Lakshmanan, "Exact soliton solutions of coupled nonlinear Schrödinger equations: shape changing collisions, logic gates, and partially coherent solitons," Phys. Rev. E 67, 046617 (2003).
[CrossRef]

A. A. Sukhorukov and N. N. Akhmediev, "Multiport soliton devices with controllable transmission," Opt. Lett. 28, 908-910 (2003).
[CrossRef] [PubMed]

2001 (4)

C. Anastassiou, J. W. Fleischer, T. Carmon, M. Segev, and K. Steiglitz, "Information transfer through cascaded collisions of vector solitons," Opt. Lett. 26, 1498-1500 (2001).
[CrossRef]

J. Yang, "Interactions of vector solitons," Phys. Rev. E 64, 026607 (2001).
[CrossRef]

P. Tchofo Dinda, K. Nakkeeran, and A. B. Moubissi, "Collective variable theory for optical solitons in fibers," Phys. Rev. E 64, 016608 (2001).
[CrossRef]

T. Kanna and M. Lakshmanan, "Exact soliton solutions, shape changing collisions, and partially coherent solitons in coupled nonlinear Schrödinger equations," Phys. Rev. Lett. 86, 5043-5046 (2001).
[CrossRef] [PubMed]

2000 (1)

K. Steiglitz, "Time-gated Manakov spatial solitons are computationally universal," Phys. Rev. E 63, 016608 (2000).
[CrossRef]

1999 (1)

J. Yang, "Multisoliton perturbation theory for the Manakov equations and its applications to nonlinear optics," Phys. Rev. E 59, 2393-2405 (1999).
[CrossRef]

1998 (1)

M. H. Jakubowski, K. Steiglitz, and R. Squier, "State transformations of colliding optical solitons and possible application to computation in bulk media," Phys. Rev. E 58, 6752-6758 (1998).
[CrossRef]

1997 (5)

R. Radhakrishnan, M. Lakshmanan, and J. Hietarinta, "Inelastic collision and switching of coupled bright solitons in optical fibers," Phys. Rev. E 56, 2213-2216 (1997).
[CrossRef]

Y. Bard and Y. Silberberg, "Polarization evolution and polarization instability of solitons in birefringent optical fibers," Phys. Rev. Lett. 78, 3290-3293 (1997).
[CrossRef]

V. S. Schesnovich and E. V. Doktorov, "Perturbation theory for solitons of the Manakov system," Phys. Rev. E 55, 7626-7635 (1997).
[CrossRef]

T. I. Lakoba and D. J. Kaup, "Perturbation theory for the Manakov soliton and its applications to pulse propagation in randomly birefringent fibers," Phys. Rev. E 56, 6147-6165 (1997).
[CrossRef]

Z. Chen, M. Segev, T. H. Coskun, D. N. Christodoulides, and Y. S. Kivshar, "Coupled photorefractive spatial-soliton pairs," J. Opt. Soc. Am. B 14, 3066-3077 (1997).
[CrossRef]

1996 (2)

P. Tchofo Dinda, G. Millot, E. Seve, and M. Haelterman, "Demonstration of a nonlinear gap in the modulational instability spectra of wave propagation in highly birefringent fibers," Opt. Lett. 21, 1640-1642 (1996).
[CrossRef]

J. U. Kang, G. I. Stegeman, J. S. Aitchison, and N. Akhmediev, "Observation of Manakov spatial solitons in AlGaAs planar waveguides," Phys. Rev. Lett. 76, 3699-3702 (1996).
[CrossRef] [PubMed]

1983 (1)

D. Anderson, "Variational approach to nonlinear pulse propagation in optical fibers," Phys. Rev. A 27, 3135-3145 (1983).
[CrossRef]

1981 (2)

Y. Kodama and M. J. Ablowitz, "Perturbations of solitons and solitary waves," Stud. Appl. Math. 64, 225-245 (1981).

V. I. Karpman and V. V. Solovev, "A perturbational approach to the two soliton system," Physica D 3, 487-502 (1981).
[CrossRef]

1974 (1)

S. V. Manakov, "On the theory of two-dimensional stationary self-focusing of electomagnetic waves," Sov. Phys. JETP 38, 248-253 (1974).

Ablowitz, M. J.

M. J. Ablowitz, B. Prinari, and A. D. Trubatch, "Soliton interaction in the vector NLS equations," Inverse Probl. 20, 1217-1237 (2004).
[CrossRef]

Y. Kodama and M. J. Ablowitz, "Perturbations of solitons and solitary waves," Stud. Appl. Math. 64, 225-245 (1981).

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, 1995).

Yu. S. Kivshar and G. P. Agrawal, Optical Solitons, 2nd ed. (Academic, 2003).

Aitchison, J. S.

J. U. Kang, G. I. Stegeman, J. S. Aitchison, and N. Akhmediev, "Observation of Manakov spatial solitons in AlGaAs planar waveguides," Phys. Rev. Lett. 76, 3699-3702 (1996).
[CrossRef] [PubMed]

Akhmediev, N.

J. U. Kang, G. I. Stegeman, J. S. Aitchison, and N. Akhmediev, "Observation of Manakov spatial solitons in AlGaAs planar waveguides," Phys. Rev. Lett. 76, 3699-3702 (1996).
[CrossRef] [PubMed]

Akhmediev, N. N.

Anastassiou, C.

Anderson, D.

D. Anderson, "Variational approach to nonlinear pulse propagation in optical fibers," Phys. Rev. A 27, 3135-3145 (1983).
[CrossRef]

Babarro, J.

J. Babarro, M. J. Paz-alonso, H. Michinel, J. R. Salgueiro, and D. N. Olivieri, "Controllable scattering of vector Bose-Einstein solitons," Phys. Rev. A 71, 043608 (2005).
[CrossRef]

Bard, Y.

Y. Bard and Y. Silberberg, "Polarization evolution and polarization instability of solitons in birefringent optical fibers," Phys. Rev. Lett. 78, 3290-3293 (1997).
[CrossRef]

Carmon, T.

Chen, Z.

Christodoulides, D. N.

Coskun, T. H.

Doktorov, E. V.

V. S. Schesnovich and E. V. Doktorov, "Perturbation theory for solitons of the Manakov system," Phys. Rev. E 55, 7626-7635 (1997).
[CrossRef]

Feigenbaum, E.

Fleischer, J. W.

Haelterman, M.

Hasegawa, A.

A. Hasegawa and Y. Kodama, Solitons in Optical Communications (Oxford U. Press, 1995).

Hietarinta, J.

R. Radhakrishnan, M. Lakshmanan, and J. Hietarinta, "Inelastic collision and switching of coupled bright solitons in optical fibers," Phys. Rev. E 56, 2213-2216 (1997).
[CrossRef]

Jakubowski, M. H.

M. H. Jakubowski, K. Steiglitz, and R. Squier, "State transformations of colliding optical solitons and possible application to computation in bulk media," Phys. Rev. E 58, 6752-6758 (1998).
[CrossRef]

Kang, J. U.

J. U. Kang, G. I. Stegeman, J. S. Aitchison, and N. Akhmediev, "Observation of Manakov spatial solitons in AlGaAs planar waveguides," Phys. Rev. Lett. 76, 3699-3702 (1996).
[CrossRef] [PubMed]

Kanna, T.

T. Kanna and M. Lakshmanan, "Exact soliton solutions of coupled nonlinear Schrödinger equations: shape changing collisions, logic gates, and partially coherent solitons," Phys. Rev. E 67, 046617 (2003).
[CrossRef]

T. Kanna and M. Lakshmanan, "Exact soliton solutions, shape changing collisions, and partially coherent solitons in coupled nonlinear Schrödinger equations," Phys. Rev. Lett. 86, 5043-5046 (2001).
[CrossRef] [PubMed]

Karpman, V. I.

V. I. Karpman and V. V. Solovev, "A perturbational approach to the two soliton system," Physica D 3, 487-502 (1981).
[CrossRef]

Kaup, D. J.

T. I. Lakoba and D. J. Kaup, "Perturbation theory for the Manakov soliton and its applications to pulse propagation in randomly birefringent fibers," Phys. Rev. E 56, 6147-6165 (1997).
[CrossRef]

Kivshar, Y. S.

Kivshar, Yu. S.

Yu. S. Kivshar and G. P. Agrawal, Optical Solitons, 2nd ed. (Academic, 2003).

Kodama, Y.

Y. Kodama and M. J. Ablowitz, "Perturbations of solitons and solitary waves," Stud. Appl. Math. 64, 225-245 (1981).

A. Hasegawa and Y. Kodama, Solitons in Optical Communications (Oxford U. Press, 1995).

Lakoba, T. I.

T. I. Lakoba and D. J. Kaup, "Perturbation theory for the Manakov soliton and its applications to pulse propagation in randomly birefringent fibers," Phys. Rev. E 56, 6147-6165 (1997).
[CrossRef]

Lakshmanan, M.

T. Kanna and M. Lakshmanan, "Exact soliton solutions of coupled nonlinear Schrödinger equations: shape changing collisions, logic gates, and partially coherent solitons," Phys. Rev. E 67, 046617 (2003).
[CrossRef]

T. Kanna and M. Lakshmanan, "Exact soliton solutions, shape changing collisions, and partially coherent solitons in coupled nonlinear Schrödinger equations," Phys. Rev. Lett. 86, 5043-5046 (2001).
[CrossRef] [PubMed]

R. Radhakrishnan, M. Lakshmanan, and J. Hietarinta, "Inelastic collision and switching of coupled bright solitons in optical fibers," Phys. Rev. E 56, 2213-2216 (1997).
[CrossRef]

Lazarides, N.

N. Lazarides and G. P. Tsironis, "Coupled nonlinear Schrödinger field equations for electromagnetic wave propagation in nonlinear left-handed materials," Phys. Rev. E 71, 036614 (2005).
[CrossRef]

Manakov, S. V.

S. V. Manakov, "On the theory of two-dimensional stationary self-focusing of electomagnetic waves," Sov. Phys. JETP 38, 248-253 (1974).

Michinel, H.

J. Babarro, M. J. Paz-alonso, H. Michinel, J. R. Salgueiro, and D. N. Olivieri, "Controllable scattering of vector Bose-Einstein solitons," Phys. Rev. A 71, 043608 (2005).
[CrossRef]

Millot, G.

R. Radhakrishnan, P. Tchofo Dinda, and G. Millot, "Efficient control of the energy-exchange due to the Manakov vector-soliton collision," Phys. Rev. E 69, 046607 (2003).
[CrossRef]

P. Tchofo Dinda, G. Millot, E. Seve, and M. Haelterman, "Demonstration of a nonlinear gap in the modulational instability spectra of wave propagation in highly birefringent fibers," Opt. Lett. 21, 1640-1642 (1996).
[CrossRef]

Moubissi, A. B.

P. Tchofo Dinda, K. Nakkeeran, and A. B. Moubissi, "Collective variable theory for optical solitons in fibers," Phys. Rev. E 64, 016608 (2001).
[CrossRef]

Nakkeeran, K.

P. Tchofo Dinda, K. Nakkeeran, and A. B. Moubissi, "Collective variable theory for optical solitons in fibers," Phys. Rev. E 64, 016608 (2001).
[CrossRef]

Olivieri, D. N.

J. Babarro, M. J. Paz-alonso, H. Michinel, J. R. Salgueiro, and D. N. Olivieri, "Controllable scattering of vector Bose-Einstein solitons," Phys. Rev. A 71, 043608 (2005).
[CrossRef]

Orenstein, M.

Paz-alonso, M. J.

J. Babarro, M. J. Paz-alonso, H. Michinel, J. R. Salgueiro, and D. N. Olivieri, "Controllable scattering of vector Bose-Einstein solitons," Phys. Rev. A 71, 043608 (2005).
[CrossRef]

Prinari, B.

M. J. Ablowitz, B. Prinari, and A. D. Trubatch, "Soliton interaction in the vector NLS equations," Inverse Probl. 20, 1217-1237 (2004).
[CrossRef]

Radhakrishnan, R.

R. Radhakrishnan, P. Tchofo Dinda, and G. Millot, "Efficient control of the energy-exchange due to the Manakov vector-soliton collision," Phys. Rev. E 69, 046607 (2003).
[CrossRef]

R. Radhakrishnan, M. Lakshmanan, and J. Hietarinta, "Inelastic collision and switching of coupled bright solitons in optical fibers," Phys. Rev. E 56, 2213-2216 (1997).
[CrossRef]

Salgueiro, J. R.

J. Babarro, M. J. Paz-alonso, H. Michinel, J. R. Salgueiro, and D. N. Olivieri, "Controllable scattering of vector Bose-Einstein solitons," Phys. Rev. A 71, 043608 (2005).
[CrossRef]

Schesnovich, V. S.

V. S. Schesnovich and E. V. Doktorov, "Perturbation theory for solitons of the Manakov system," Phys. Rev. E 55, 7626-7635 (1997).
[CrossRef]

Segev, M.

Seve, E.

Silberberg, Y.

Y. Bard and Y. Silberberg, "Polarization evolution and polarization instability of solitons in birefringent optical fibers," Phys. Rev. Lett. 78, 3290-3293 (1997).
[CrossRef]

Solovev, V. V.

V. I. Karpman and V. V. Solovev, "A perturbational approach to the two soliton system," Physica D 3, 487-502 (1981).
[CrossRef]

Squier, R.

M. H. Jakubowski, K. Steiglitz, and R. Squier, "State transformations of colliding optical solitons and possible application to computation in bulk media," Phys. Rev. E 58, 6752-6758 (1998).
[CrossRef]

Stegeman, G. I.

J. U. Kang, G. I. Stegeman, J. S. Aitchison, and N. Akhmediev, "Observation of Manakov spatial solitons in AlGaAs planar waveguides," Phys. Rev. Lett. 76, 3699-3702 (1996).
[CrossRef] [PubMed]

Steiglitz, K.

C. Anastassiou, J. W. Fleischer, T. Carmon, M. Segev, and K. Steiglitz, "Information transfer through cascaded collisions of vector solitons," Opt. Lett. 26, 1498-1500 (2001).
[CrossRef]

K. Steiglitz, "Time-gated Manakov spatial solitons are computationally universal," Phys. Rev. E 63, 016608 (2000).
[CrossRef]

M. H. Jakubowski, K. Steiglitz, and R. Squier, "State transformations of colliding optical solitons and possible application to computation in bulk media," Phys. Rev. E 58, 6752-6758 (1998).
[CrossRef]

Sukhorukov, A. A.

Tchofo Dinda, P.

R. Radhakrishnan, P. Tchofo Dinda, and G. Millot, "Efficient control of the energy-exchange due to the Manakov vector-soliton collision," Phys. Rev. E 69, 046607 (2003).
[CrossRef]

P. Tchofo Dinda, K. Nakkeeran, and A. B. Moubissi, "Collective variable theory for optical solitons in fibers," Phys. Rev. E 64, 016608 (2001).
[CrossRef]

P. Tchofo Dinda, G. Millot, E. Seve, and M. Haelterman, "Demonstration of a nonlinear gap in the modulational instability spectra of wave propagation in highly birefringent fibers," Opt. Lett. 21, 1640-1642 (1996).
[CrossRef]

Trubatch, A. D.

M. J. Ablowitz, B. Prinari, and A. D. Trubatch, "Soliton interaction in the vector NLS equations," Inverse Probl. 20, 1217-1237 (2004).
[CrossRef]

Tsironis, G. P.

N. Lazarides and G. P. Tsironis, "Coupled nonlinear Schrödinger field equations for electromagnetic wave propagation in nonlinear left-handed materials," Phys. Rev. E 71, 036614 (2005).
[CrossRef]

Yang, J.

J. Yang, "Interactions of vector solitons," Phys. Rev. E 64, 026607 (2001).
[CrossRef]

J. Yang, "Multisoliton perturbation theory for the Manakov equations and its applications to nonlinear optics," Phys. Rev. E 59, 2393-2405 (1999).
[CrossRef]

Inverse Probl. (1)

M. J. Ablowitz, B. Prinari, and A. D. Trubatch, "Soliton interaction in the vector NLS equations," Inverse Probl. 20, 1217-1237 (2004).
[CrossRef]

J. Opt. Soc. Am. B (2)

Opt. Lett. (3)

Phys. Rev. A (2)

D. Anderson, "Variational approach to nonlinear pulse propagation in optical fibers," Phys. Rev. A 27, 3135-3145 (1983).
[CrossRef]

J. Babarro, M. J. Paz-alonso, H. Michinel, J. R. Salgueiro, and D. N. Olivieri, "Controllable scattering of vector Bose-Einstein solitons," Phys. Rev. A 71, 043608 (2005).
[CrossRef]

Phys. Rev. E (11)

M. H. Jakubowski, K. Steiglitz, and R. Squier, "State transformations of colliding optical solitons and possible application to computation in bulk media," Phys. Rev. E 58, 6752-6758 (1998).
[CrossRef]

R. Radhakrishnan, M. Lakshmanan, and J. Hietarinta, "Inelastic collision and switching of coupled bright solitons in optical fibers," Phys. Rev. E 56, 2213-2216 (1997).
[CrossRef]

N. Lazarides and G. P. Tsironis, "Coupled nonlinear Schrödinger field equations for electromagnetic wave propagation in nonlinear left-handed materials," Phys. Rev. E 71, 036614 (2005).
[CrossRef]

R. Radhakrishnan, P. Tchofo Dinda, and G. Millot, "Efficient control of the energy-exchange due to the Manakov vector-soliton collision," Phys. Rev. E 69, 046607 (2003).
[CrossRef]

T. Kanna and M. Lakshmanan, "Exact soliton solutions of coupled nonlinear Schrödinger equations: shape changing collisions, logic gates, and partially coherent solitons," Phys. Rev. E 67, 046617 (2003).
[CrossRef]

K. Steiglitz, "Time-gated Manakov spatial solitons are computationally universal," Phys. Rev. E 63, 016608 (2000).
[CrossRef]

P. Tchofo Dinda, K. Nakkeeran, and A. B. Moubissi, "Collective variable theory for optical solitons in fibers," Phys. Rev. E 64, 016608 (2001).
[CrossRef]

V. S. Schesnovich and E. V. Doktorov, "Perturbation theory for solitons of the Manakov system," Phys. Rev. E 55, 7626-7635 (1997).
[CrossRef]

T. I. Lakoba and D. J. Kaup, "Perturbation theory for the Manakov soliton and its applications to pulse propagation in randomly birefringent fibers," Phys. Rev. E 56, 6147-6165 (1997).
[CrossRef]

J. Yang, "Multisoliton perturbation theory for the Manakov equations and its applications to nonlinear optics," Phys. Rev. E 59, 2393-2405 (1999).
[CrossRef]

J. Yang, "Interactions of vector solitons," Phys. Rev. E 64, 026607 (2001).
[CrossRef]

Phys. Rev. Lett. (3)

T. Kanna and M. Lakshmanan, "Exact soliton solutions, shape changing collisions, and partially coherent solitons in coupled nonlinear Schrödinger equations," Phys. Rev. Lett. 86, 5043-5046 (2001).
[CrossRef] [PubMed]

Y. Bard and Y. Silberberg, "Polarization evolution and polarization instability of solitons in birefringent optical fibers," Phys. Rev. Lett. 78, 3290-3293 (1997).
[CrossRef]

J. U. Kang, G. I. Stegeman, J. S. Aitchison, and N. Akhmediev, "Observation of Manakov spatial solitons in AlGaAs planar waveguides," Phys. Rev. Lett. 76, 3699-3702 (1996).
[CrossRef] [PubMed]

Physica D (1)

V. I. Karpman and V. V. Solovev, "A perturbational approach to the two soliton system," Physica D 3, 487-502 (1981).
[CrossRef]

Sov. Phys. JETP (1)

S. V. Manakov, "On the theory of two-dimensional stationary self-focusing of electomagnetic waves," Sov. Phys. JETP 38, 248-253 (1974).

Stud. Appl. Math. (1)

Y. Kodama and M. J. Ablowitz, "Perturbations of solitons and solitary waves," Stud. Appl. Math. 64, 225-245 (1981).

Other (3)

Yu. S. Kivshar and G. P. Agrawal, Optical Solitons, 2nd ed. (Academic, 2003).

G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, 1995).

A. Hasegawa and Y. Kodama, Solitons in Optical Communications (Oxford U. Press, 1995).

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Figures (18)

Fig. 1
Fig. 1

Evolution of the parameters of the components of two colliding VSs, in the Manakov system without fiber losses for U 1 mode. The initial VS parameters are given in the text. Δ f = 0.053 THz .

Fig. 2
Fig. 2

Evolution of the soliton parameters for the U 2 mode for the system considered in Fig. 1.

Fig. 3
Fig. 3

Evolution of the parameters of the components of two colliding VSs, in the Manakov system in the presence of fiber losses for U 1 mode. α = 0.2 dB km , Δ f = 0.053 THz . The initial VS parameters are given in the text.

Fig. 4
Fig. 4

Evolution of the soliton parameters for the U 2 mode for the system considered in Fig. 3.

Fig. 5
Fig. 5

Evolution of the parameters for two colliding VSs in the presence of fiber losses U 1 mode. The initial VS parameters are given in the text. α = 0.6 db km , Δ f = 0.053 THz .

Fig. 6
Fig. 6

Evolution of the soliton parameters for the U 2 mode for the system considered in Fig. 5.

Fig. 7
Fig. 7

Evolution of the parameters for two colliding VSs in the absence of fiber losses for the U 1 mode. The initial VS parameters are given in the text. Δ f = 0.0132 THz .

Fig. 8
Fig. 8

Evolution of the soliton parameters for the U 2 mode for the system considered in Fig. 7.

Fig. 9
Fig. 9

Evolution of the parameters for two colliding VSs, in the presence of fiber losses for the U 1 mode. The initial VS parameters are given in the text. α = 0.2 dB km ; Δ f = 0.0132 THz .

Fig. 10
Fig. 10

Evolution of the soliton parameters for the U 2 mode for the system considered in Fig. 9.

Fig. 11
Fig. 11

Evolution of the parameters for two colliding VSs in the absence of fiber losses for the U 1 mode. The initial VS parameters are given in the text. Δ f = 0.0088 THz .

Fig. 12
Fig. 12

Evolution of the soliton parameters for the U 2 mode, for the system considered in Fig. 11.

Fig. 13
Fig. 13

Evolution of the parameters for two colliding VSs, in the presence of fiber losses for the U 1 mode. The initial VS parameters are given in the text. α = 0.2 dB km ; Δ f = 0.0088 THz .

Fig. 14
Fig. 14

Evolution of the soliton parameters for the U 2 mode for the system considered in Fig. 13.

Fig. 15
Fig. 15

Evolution of the parameters for two colliding VSs in the presence of a modified XPM ( B = 2 3 ) , without fiber losses, for the U 1 mode. The initial VS parameters are given in the text. Δ f = 0.016 THz .

Fig. 16
Fig. 16

Evolution of the soliton parameters for the U 2 mode for the system considered in Fig. 15.

Fig. 17
Fig. 17

Evolution of the parameters for two colliding VSs, in the presence of a modified XPM ( B = 2 3 ) and fiber losses ( α = 0.2 dB km ) , for the U 1 mode. The initial VS parameters are given in the text. Δ f = 0.016 THz .

Fig. 18
Fig. 18

Evolution of the soliton parameters for the U 2 mode for the system considered in Fig. 17.

Equations (30)

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U l z + i ( β 2 2 ) 2 U l t 2 i γ ( U l 2 + U 3 l 2 ) U l = ( α 2 ) U l , l = 1 , 2 ,
U 1 = P cos ( θ ) exp ( i ϕ 1 ) sech ( η 1 R ) exp ( i η 1 I ) ,
U 2 = P sin ( θ ) exp ( i ϕ 2 ) sech ( η 1 R ) exp ( i η 1 I ) ,
η 1 R = k 1 R ( t + t 0 ) , η 1 I = k 1 I t + η 0 .
U m ( z , t ) = f m ( X 1 , X 2 , , X N , t ) + q m ( z , t ) , m = 1 , 2 ,
f ( l ) = ( f 1 ( l ) f 2 ( l ) ) , l = 1 , 2 ,
f m = f m ( 1 ) + f m ( 2 ) , m = 1 , 2 .
f ± ( t , z ) = X 1 exp [ ( t ± X 2 ) 2 X 3 2 + i X 4 2 ( t ± X 2 ) 2 i X 5 ( t ± X 2 ) + i X 6 ] .
X ̇ 1 = 1 2 β 2 X 1 X 4 1 2 α X 1 ,
X ̇ 2 = β 2 X 5 ,
X ̇ 3 = β 2 X 3 X 4 ,
X ̇ 4 = β 2 ( 4 X 3 4 X 4 2 ) 2 γ X 1 2 X 3 2 B γ 2 4 X 3 4 ( 4 X 1 2 X 3 2 32 X 1 2 X 2 2 ) exp ( 4 X 2 2 X 3 2 ) ,
X ̇ 5 = 2 2 B γ X 1 2 X 2 X 3 2 exp ( 4 X 2 2 X 3 2 ) ,
X ̇ 6 = β 2 ( X 5 2 2 1 X 3 2 ) + 5 γ x 1 2 4 2 + B γ X 1 2 16 X 3 2 ( 102 X 3 2 162 X 2 2 ) exp ( 4 X 2 2 X 3 2 ) .
X ̇ 1 = 1 2 β 2 X 1 X 4 1 2 α X 1 ,
X ̇ 2 = 0 ,
X ̇ 3 = β 2 X 3 X 4 ,
X ̇ 4 = 2 γ X 1 2 X 3 2 2 B γ X 1 2 X 3 2 β 2 ( 4 X 3 4 X 4 2 ) ,
X ̇ 5 = 0 ,
X ̇ 6 = β 2 X 3 2 + 5 γ X 1 2 4 2 + B γ 16 ( 102 X 1 2 ) .
Λ m q m 2 d t = u m f m ( X 1 , X 2 , , X N , t ) 2 d t , m = 1 , 2 .
C j m = d Λ m d X j 0 .
C j m = Λ m X j = R [ q m f m * X j ] d t = 0 , ( j = 1 , 2 , , 6 )
f m ( l ) = x 1 m ( l ) sech ( t x 2 m ( l ) x 3 m ( l ) ) exp [ i x 4 m ( l ) ( t x 2 m ( l ) ) 2 2 i x 5 m ( l ) ( t x 2 m ( l ) ) + i x 6 m ( l ) ] , l , m = 1 , 2 ,
x 11 ( l ) = x 12 ( l ) = 0.25 W 1 2 , x 21 ( 1 ) = x 22 ( 1 ) = x 21 ( 2 ) = x 22 ( 2 ) = 12 ps , x 31 ( l ) = x 32 ( l ) = 2 ps ,
x 4 m ( l ) = x 4 m ( l ) = 0 THz ps , x 51 ( 1 ) 2 π = x 52 ( 1 ) 2 π = x 51 ( 2 ) 2 π = x 52 ( 2 ) 2 π = 0.0066 THz , l , m = 1 , 2 .
x 11 ( l ) = x 12 ( l ) = 0.16667 W 1 2 , x 21 ( 1 ) = x 22 ( 1 ) = x 21 ( 2 ) = x 22 ( 2 ) = 18 ps , x 31 ( l ) = x 32 ( l ) = 3 ps ,
x 4 m ( l ) = x 4 m ( l ) = 0 THz ps , x 51 ( 1 ) 2 π = x 52 ( 1 ) 2 π = x 51 ( 2 ) 2 π = x 52 ( 2 ) 2 π = 0.0044 THz , l , m = 1 , 2 .
x 11 ( l ) = x 12 ( l ) = 0.25 W 1 2 , x 21 ( 1 ) = x 22 ( 1 ) = x 21 ( 2 ) = x 22 ( 2 ) = 12 ps , x 31 ( l ) = x 32 ( l ) = 2 ps ,
x 4 m ( l ) = x 4 m ( l ) = 0 THz ps , x 51 ( 1 ) 2 π = x 52 ( 1 ) 2 π = x 51 ( 2 ) 2 π = x 52 ( 2 ) 2 π = 0.008 THz , l , m = 1 , 2 .

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